Could be either asphalt asbestos, vinyl asbestos or rubber tile that was improperly installed with cutback type adhesive.

A professional would slice off the adhesive with sharp razor scrapers and then sand the remainder off. Does the adhesive contain asbestos? Probably. Is that a problem? Probably not, but you have to make that decision for yourself.

It would be silly to give up on your hardwood, especially if it is very decent lumber to begin with. However, that said, you may want to remove it all and install new. It would avoid your having to deal with the asphaltic adhesive removal.